An extension of Borel-Laplace methods and monomial summability

TL;DR

This paper extends Borel-Laplace methods to characterize monomial summability via parameter-dependent integral transforms and applies this to establish 1-summability of formal solutions in certain PDEs.

Contribution

It introduces a new characterization of monomial summability using Borel-Laplace type integrals with a parameter, advancing the understanding of summability in PDE solutions.

Findings

Monomial summability characterized by parameter-dependent Borel-Laplace integrals

Formal solutions of PDEs shown to be 1-summable in a monomial

New techniques for analyzing summability in partial differential equations

Abstract

In this paper we will show that monomial summability can be characterized using Borel-Laplace like integral transformations depending of a parameter $0<s<1$. We will apply this result to prove 1-summability in a monomial of formal solutions of a family of partial differential equations.